Why is it that if the centripetal force on an object increases, its acceleration increases?(1 point) Responses
A. Its velocity increases.
B. Its mass increases.
C. Its mass decreases.
D. Its velocity decreases.
A. Its velocity increases.
A is correct
The correct answer is A. Its velocity increases.
According to the centripetal force formula, F = m * a, where F is the centripetal force, m is the mass of the object, and a is the acceleration.
If the centripetal force on an object increases, and the mass remains constant, then the only way for the equation to hold true is for the acceleration (a) to increase.
This increase in acceleration means that the object is moving faster, which is represented by an increase in its velocity. Therefore, if the centripetal force on an object increases, its velocity increases as well.
The correct answer is A. Its velocity increases.
When the centripetal force on an object increases, its acceleration also increases. This is because the centripetal force is responsible for changing the direction of the object's velocity, causing it to move in a circular path.
To understand why this happens, we need to know the formula for centripetal force:
F = m * a_c
where F is the centripetal force, m is the mass of the object, and a_c is the centripetal acceleration.
From this formula, we can see that the centripetal force is directly proportional to the mass of the object. That means, if the centripetal force increases, the mass of the object does not change. So, option B (Its mass increases) and C (Its mass decreases) are not correct.
On the other hand, the formula also tells us that the centripetal force is directly proportional to the centripetal acceleration. Therefore, if the centripetal force increases, the centripetal acceleration must also increase. And since acceleration is the rate at which velocity changes, an increase in acceleration means the velocity of the object is increasing as well. This is why option A (Its velocity increases) is the correct answer.
Option D (Its velocity decreases) is incorrect because an increase in the centripetal force would result in an increase in the velocity, not a decrease.